Control system for throttle valve actuating device

ABSTRACT

A control system for a throttle valve actuating device is disclosed. The throttle valve actuating device includes a throttle valve of an internal combustion engine and an actuator for actuating the throttle valve. The control system includes a predictor for predicting a future throttle valve opening and controls the throttle actuating device according to the throttle valve opening predicted by the predictor so that the throttle valve opening coincides with a target opening.

RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/043,625, filed on Jan. 10, 2002, and entitled “CONTROL SYSTEM FORPLANT” now abandoned.

BACKGROUND OF THE INVENTION

The present invention relates to a control system for a throttle valveactuating device including a throttle valve of an internal combustionengine and an actuator for actuating the throttle valve.

One known control system for controlling a throttle valve actuatingdevice including a motor for actuating the throttle valve and springsfor energizing the throttle valve is disclosed in Japanese PatentLaid-open No. Hei 8-261050. In this control system, the throttle valveactuating device is controlled with a PID (Proportional, Integral, andDifferential) control according to a throttle valve opening detected bya throttle valve opening sensor.

Since the throttle valve actuating device includes a dead time elementwhich delays the throttle valve movement, the PID control by theabove-described conventional control system may easily become unstableif the control gain of the PID control according to the detectedthrottle valve opening is set to a large value. Therefore, it isnecessary to set the control gain to a value which is sufficiently smallso that the control may not become unstable. However, this results in alow response speed.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a controlsystem for a throttle valve actuating device, which can improve theresponse speed by expanding the stability margin of the control.

To achieve the above object, the present invention provides a controlsystem for a throttle valve actuating device (10) including a throttlevalve (3) of an internal combustion engine and actuating means (6) foractuating the throttle valve (3). The control system includes predictingmeans (23) for predicting a future throttle valve opening (PREDTH) andcontrols the throttle actuating device (10) according to the throttlevalve opening (PREDTH) predicted by the predicting means (23) so thatthe throttle valve opening (TH) coincides with a target opening (THR).

With this configuration, the throttle actuating device is controlledaccording to the future throttle valve opening predicted by thepredicting means. Accordingly, the stability margin of the control canbe expanded although the throttle valve actuating device includes a deadtime element. As a result, the control gain can be set to a larger valueto thereby improve the control response speed.

Preferably, the throttle valve actuating device (10) is modeled to acontrolled object model which includes a dead time element, and thepredicting means (23) predicts a throttle valve opening after the elapseof a dead time (d) due to the dead time element, based on the controlledobject model.

With this configuration, the throttle valve actuating device (10) ismodeled to the controlled object model including a dead time element,and the throttle valve opening after the elapse of a dead time ispredicted based on the controlled object model. Accordingly,compensation of the dead time in the throttle valve actuating device canaccurately be performed.

Preferably, the control system further includes identifying means (22)for identifying at least one model parameter (a1, a2, b1, c1) of thecontrolled object model. The predicting means (23) predicts the throttlevalve opening (PREDTH) using the at least one model parameter (a1, a2,b1, c1) identified by the identifying means (22).

With this configuration, the throttle valve opening is predicted usingone or more model parameter identified by the identifying means.Accordingly, it is possible to calculate an accurate predicted throttlevalve opening even when the dynamic characteristic of the throttle valveactuating device has changed due to aging or a change in theenvironmental condition.

Preferably, the control system further includes a sliding modecontroller (21) for controlling the throttle valve actuating device (10)with a sliding mode control according to a throttle valve opening(PREDTH) predicted by the predicting means (23).

With this configuration, the throttle valve actuating device iscontrolled with the sliding mode control having good robustness.Accordingly, good stability and controllability of the control can bemaintained even when there exists a modeling error (a difference betweenthe characteristics of the actual plant and the characteristics of thecontrolled object model) due to a difference between the actual deadtime of the throttle valve actuating device and the dead time of thecontrolled object model.

Preferably, the sliding mode controller (21) controls the throttle valveactuating device (10) using the at least one model parameter (a1, a2,b1, c1) identified by the identifying means (22).

With this configuration, the throttle valve actuating device iscontrolled by the sliding mode controller using one or more modelparameter identified by the identifying means. Accordingly, the modelingerror can be made smaller so that the controllability is furtherimproved.

Preferably, the control input (Usl) from the sliding mode controller(21) to the throttle valve actuating device (10) includes an adaptivelaw input (Uadp).

With this configuration, better controllability is obtained even in thepresence of disturbance and/or the modeling error.

The above and other objects, features, and advantages of the presentinvention will become apparent from the following description when takenin conjunction with the accompanying drawings which illustrateembodiments of the present invention by way of example.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a throttle valve control system accordingto a first embodiment of the present invention;

FIGS. 2A and 2B are diagrams showing frequency characteristics of thethrottle valve actuating device shown in FIG. 1;

FIG. 3 is a functional block diagram showing functions realized by anelectronic control unit (ECU) shown in FIG. 1;

FIG. 4 is a diagram showing the relationship between controlcharacteristics of a sliding mode controller and the value of aswitching function setting parameter (VPOLE);

FIG. 5 is a diagram showing a range for setting control gains (F, G) ofthe sliding mode controller;

FIGS. 6A and 6B are diagrams illustrative of a drift of modelparameters;

FIGS. 7A through 7C are diagrams showing functions for correcting anidentifying error;

FIG. 8 is a diagram illustrating that a default opening deviation of athrottle valve is reflected to a model parameter (c1′);

FIG. 9 is a flowchart showing a throttle valve opening control process;

FIG. 10 is a flowchart showing a process of setting state variables inthe process shown in FIG. 9;

FIG. 11 is a flowchart showing a process of performing calculations of amodel parameter identifier in the process shown in FIG. 9;

FIG. 12 is a flowchart showing a process of calculating an identifyingerror (ide) in the process shown in FIG. 11;

FIGS. 13A and 13B are diagrams illustrative of a process of low-passfiltering on the identifying error (ide);

FIG. 14 is a flowchart showing the dead zone process in the processshown in FIG. 12;

FIG. 15 is a diagram showing a table used in the process shown in FIG.14;

FIG. 16 is a flowchart showing a process of stabilizing a modelparameter vector (θ) in the process shown in FIG. 11;

FIG. 17 is a flowchart showing a limit process of model parameters (a1′,a2′) in the process shown in FIG. 16;

FIG. 18 is a diagram illustrative of the change in the values of themodel parameters in the process shown in FIG. 16;

FIG. 19 is a flowchart showing a limit process of a model parameter(b1′) in the process shown in FIG. 16;

FIG. 20 is a flowchart showing a limit process of a model parameter(c1′) in the process shown in FIG. 16;

FIG. 21 is a flowchart showing a process of performing calculations of astate predictor in the process shown in FIG. 9;

FIG. 22 is a flowchart showing a process of calculating a control input(Usl) in the process shown in FIG. 9;

FIG. 23 is a flowchart showing a process of calculating a predictedswitching function value (σpre) in the process shown in FIG. 22;

FIG. 24 is a flowchart showing a process of calculating the switchingfunction setting parameter (VPOLE) in the process shown in FIG. 23;

FIGS. 25A through 25C are diagrams showing maps used in the processshown in FIG. 24;

FIG. 26 is a flowchart showing a process of calculating an integratedvalue of the predicted switching function value (σpre) in the processshown in FIG. 22;

FIG. 27 is a flowchart showing a process of calculating a reaching lawinput (Urch) in the process shown in FIG. 22;

FIG. 28 is a flowchart showing a process of calculating an adaptive lawinput (Uadp) in the process shown in FIG. 22;

FIG. 29 is a flowchart showing a process of determining the stability ofthe sliding mode controller in the process shown in FIG. 9;

FIG. 30 is a flowchart showing a process of calculating a defaultopening deviation (thdefadp) in the process shown in FIG. 9;

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 schematically shows a configuration of a throttle valve controlsystem according to a first embodiment of the present invention. Aninternal combustion engine (hereinafter referred to as “engine”) 1 hasan intake passage 2 with a throttle valve 3 disposed therein. Thethrottle valve 3 is provided with a return spring 4 as a firstenergizing means for energizing the throttle valve 3 in a closingdirection, and a resilient member 5 as a second energizing means forenergizing the throttle valve 3 in an opening direction. The throttlevalve 3 can be actuated by a motor 6 as an actuating means through gears(not shown). When the actuating force from the motor 6 is not applied tothe throttle valve 3, an opening TH of the throttle valve 3 ismaintained at a default opening THDEF (for example, 5 degrees) where theenergizing force of the return spring 4 and the energizing force of theresilient member 5 are in equilibrium.

The motor 6 is connected to an electronic control unit (hereinafterreferred to as “ECU”) 7. The operation of the motor 6 is controlled bythe ECU 7. The throttle valve 3 is associated with a throttle valveopening sensor 8 for detecting the throttle valve opening TH. A detectedsignal from the throttle valve opening sensor 8 is supplied to the ECU7.

Further, the ECU 7 is connected to an acceleration sensor 9 fordetecting a depression amount ACC of an accelerator pedal to detect anoutput demanded by the driver of the vehicle on which the engine 1 ismounted. A detected signal from the acceleration sensor 9 is supplied tothe ECU 7.

The ECU 7 has an input circuit, an A/D converter, a central processingunit (CPU), a memory circuit, and an output circuit. The input circuitis supplied with detected signals from the throttle valve opening sensor8 and the acceleration sensor 9. The A/D converter converts inputsignals into digital signals. The CPU carries out various processoperations. The memory circuit has a ROM (read only memory) for storingprocesses executed by the CPU, and maps and tables that are referred toin the processes, a RAM for storing results of executing processes bythe CPU. The output circuit supplies an energizing current to the motor6. The ECU 7 determines a target opening THR of the throttle valve 3according to the depression amount ACC of the accelerator pedal,determines a control quantity DUT for the motor 6 in order to make thedetected throttle valve opening TH coincide with the target opening THR,and supplies an electric signal according to the control quantity DUT tothe motor 6.

In the present embodiment, a throttle valve actuating device 10 thatincludes the throttle valve 3, the return spring 4, the resilient member5, and the motor 6 is a controlled object. An input to be applied to thecontrolled object is a duty ratio DUT of the electric signal applied tothe motor 6. An output from the controlled object is the throttle valveopening TH detected by the throttle valve opening sensor 8.

When frequency response characteristics of the throttle valve actuatingdevice 10 are measured, gain characteristics and phase characteristicsindicated by the solid lines in FIGS. 2A and 2B are obtained. A modeldefined by the equation (1) shown below is set as a controlled objectmodel. Frequency response characteristics of the model are indicated bythe broken-line curves in FIGS. 2A and 2B. It has been confirmed thatthe frequency response characteristics of the model are similar to thecharacteristics of the throttle valve actuating device 10.

DTH(k+1)=a 1×DTH(k)+a 2×DTH(k−1)+b 1×DUT(k−d)+c 1  (1)

where k is a parameter representing discrete time, and DTH(k) is athrottle valve opening deviation amount defined by the equation (2)shown below. DTH(k+1) is a throttle valve opening deviation amount at adiscrete time (k+1).

DTH(k)=TH(k)−THDEF  (2)

where TH is a detected throttle valve opening, and THDEF is the defaultopening.

In the equation (1), a1, a2, b1, and c1 are parameters determining thecharacteristics of the controlled object model, and d is a dead time.The dead time is a delay between the input and output of the controlledobject model.

The model defined by the equation (1) is a DARX model (delayedautoregressive model with exogeneous input) of a discrete time system,which is employed for facilitating the application of an adaptivecontrol.

In the equation (1), the model parameter c1 which is irrelevant to theinput and output of the controlled object is employed, in addition tothe model parameters a1 and a2 which are relevant to the outputdeviation amount DTH and the model parameter b1 which is relevant to theinput duty ratio DUT. The model parameter c1 is a parameter representinga deviation amount of the default opening THDEF and disturbance appliedto the throttle valve actuating device 10. In other words, the defaultopening deviation amount and the disturbance can be identified byidentifying the model parameter c1 simultaneously with the modelparameters a1, a2, and b1 by a model parameter identifier.

FIG. 3 is a functional block diagram of the throttle valve controlsystem which is realized by the ECU 7. The throttle valve control systemas configured includes, an adaptive sliding mode controller 21, a modelparameter identifier 22, a state predictor 23 for calculating apredicted throttle valve opening deviation amount (hereinafter referredto as “predicted deviation amount” or PREDTH(k)) where PREDTH(k)(=DTH(k+d)) after the dead time d has elapsed, and a target openingsetting unit 24 for setting a target opening THR for the throttle valve3 according to the accelerator pedal depression amount ACC.

The adaptive sliding mode controller 21 calculates a duty ratio DUTaccording to an adaptive sliding mode control in order to make thedetected throttle valve opening TH coincide with the target opening THR,and outputs the calculated duty ratio DUT.

By using the adaptive sliding mode controller 21, it is possible tochange the response characteristics of the throttle valve opening TH tothe target opening THR, using a specific parameter (VPOLE). As a result,it is possible to avoid shocks at the time the throttle valve 3 movesfrom an open position to a fully closed position, i.e., at the time thethrottle valve 3 collides with a stopper for stopping the throttle valve3 in the fully closed position. It is also possible to make the engineresponse corresponding to the operation of the accelerator pedalvariable. Further, it is also possible to obtain a good stabilityagainst errors of the model parameters.

The model parameter identifier 22 calculates a corrected model parametervector θL (θL^(T)=[a1, a2, b1, c1]) and supplies the calculatedcorrected model parameter vector θL to the adaptive sliding modecontroller 21. More specifically, the model parameter identifier 22calculates a model parameter vector θ based on the throttle valveopening TH and the duty ratio DUT. The model parameter identifier 22then carries out a limit process of the model parameter vector θ tocalculate the corrected model parameter vector θL, and supplies thecorrected model parameter vector θL to the adaptive sliding modecontroller 21. In this manner, the model parameters a1, a2, and b1 whichare optimum for making the throttle valve opening TH follow up thetarget opening THR are obtained, and also the model parameter c1indicative of disturbance and a deviation amount of the default openingTHDEF is obtained.

By using the model parameter identifier 22 for identifying the modelparameters on a real-time basis, adaptation to changes in engineoperating conditions, compensation for hardware characteristicsvariations, compensatation for power supply voltage fluctuations, andadaptation to aging-dependent changes of hardware characteristics arepossible.

The state predictor 23 calculates a throttle valve opening TH (predictedvalue) after the dead time d has elapsed, or more specifically apredicted deviation amount PREDTH, based on the throttle valve openingTH and the duty ratio DUT, and supplies the calculated deviation amountPREDTH to the adaptive sliding mode controller 21. By using thepredicted deviation amount PREDTH, the robustness of the control systemagainst the dead time of the controlled object is ensured, and thecontrollability in the vicinity of the default opening THDEF where thedead time is large is improved.

Next, principles of operation of the adaptive sliding mode controller 21will be hereinafter described.

First, a target value DTHR(k) is defined as a deviation amount betweenthe target opening THR(k) and the default opening THDEF by the followingequation (3).

DTHR(k)=THR(k)−THDEF  (3)

If a deviation e(k) between the throttle valve opening deviation amountDTH and the target value DTHR is defined by the following equation (4),then a switching function value σ(k) of the adaptive sliding modecontroller is set by the following equation (5). $\begin{matrix}{{e(k)} = {{{DTH}(k)} - {{DTHR}(k)}}} & (4) \\\begin{matrix}{{\sigma (k)} = \quad {{e(k)} + {{VPOLE} \times {e\left( {k - 1} \right)}}}} \\{= \quad {{{DTH}(k)} - {{DTHR}(k)} +}} \\{\quad {{VPOLE} \times \left( {{{DTH}\left( {k - 1} \right)} - {{DTHR}\left( {k - 1} \right)}} \right)}}\end{matrix} & (5)\end{matrix}$

where VPOLE is a switching function setting parameter that is set to avalue which is greater than −1 and less than 1.

On a phase plane defined by a vertical axis representing the deviatione(k) and a horizontal axis representing the preceding deviation e(k−1),a pair of the deviation e(k) and the preceding deviation e(k−1)satisfying the equation of “σ(k)=0” represents a straight line. Thestraight line is generally referred to as a switching straight line. Asliding mode control is a control contemplating the behavior of thedeviation e(k) on the switching straight line. The sliding mode controlis carried out so that the switching function value σ(k) becomes 0,i.e., the pair of the deviation e(k) and the preceding deviation e(k−1)exists on the switching straight line on the phase plane, to therebyachieve a robust control against disturbance and the modeling error (thedifference between the characteristics of an actual plant and thecharacteristics of a controlled object model). As a result, the throttlevalve opening deviation amount DTH is controlled with good robustness tofollow up the target value DTHR.

As shown in FIG. 4, by changing the value of the switching functionsetting parameter VPOLE in the equation (5), it is possible to changedamping characteristics of the deviation e(k), i.e., the follow-upcharacteristics of the throttle valve opening deviation amount DTH tofollow the target value DTHR. Specifically, if VPOLE equals −1, then thethrottle valve opening deviation amount DTH completely fails to followup the target value DTHR. As the absolute value of the switchingfunction setting parameter VPOLE is reduced, the speed at which thethrottle valve opening deviation amount DTH follows up the target valueDTHR increases.

The throttle valve control system is required to satisfy the followingrequirements A1 and A2:

A1) When the throttle valve 3 is shifted to the fully closed position,collision of the throttle valve 3 with the stopper for stopping thethrottle valve 3 in the fully closed position should be avoided; and

A2) The controllability with respect to the nonlinear characteristics inthe vicinity of the default opening THDEF (a change in the resiliencycharacteristics due to the equilibrium between the energizing force ofthe return spring 4 and the energizing force of the resilient member 5,backlash of gears interposed between the motor 6 and the throttle valve3, and a dead zone where the throttle valve opening does not change evenwhen the duty ratio DUT changes) should be improved.

Therefore, it is necessary to lower the speed at which the deviatione(k) converges, i.e., the converging speed of the deviation e(k), in thevicinity of the fully closed position of the throttle valve, and toincrease the converging speed of the deviation e(k) in the vicinity ofthe default opening THDEF.

According to the sliding mode control, the converging speed of e(k) caneasily be changed by changing the switching function setting parameterVPOLE. Therefore in the present embodiment, the switching functionsetting parameter VPOLE is set according to the throttle valve openingTH and an amount of change DDTHR (=DTHR(k)−DTHR(k−1)) of the targetvalue DTHR, to thereby satisfy the requirements A1 and A2.

As described above, according to the sliding mode control, the deviatione(k) is converged to 0 at an indicated converging speed and robustlyagainst disturbance and the modeling error by constraining the pair ofthe deviation e(k) and the preceding deviation e(k−1) on the switchingstraight line (the pair of e(k) and e(k−1) will be hereinafter referredto as “deviation state quantity”). Therefore, in the sliding modecontrol, it is important how to place the deviation state quantity ontothe switching straight line and constrain the deviation state quantityon the switching straight line.

From the above standpoint, an input DUT(k) (also indicated as Usl(k)) tothe controlled object (an output of the controller) is expressed as thesum of an equivalent control input Ueq(k), a reaching law input Urch(k),and an adaptive law input Uadp(k), as indicated by the followingequation (6). $\begin{matrix}\begin{matrix}{{{DUT}(k)} = \quad {{Usl}(k)}} \\{= \quad {{{Ueq}(k)} + {{Urch}(k)} + {{Uadp}(k)}}}\end{matrix} & (6)\end{matrix}$

The equivalent control input Ueq(k) is an input for constraining thedeviation state quantity on the switching straight line. The reachinglaw input Urch(k) is an input for placing deviation state quantity ontothe switching straight line. The adaptive law input Uadp(k) is an inputfor placing deviation state quantity onto the switching straight linewhile reducing the modeling error and the effect of disturbance. Methodsof calculating these inputs Ueq(k), Urch(k), and Uadp(k) will bedescribed below.

Since the equivalent control input Ueq(k) is an input for constrainingthe deviation state quantity on the switching straight line, a conditionto be satisfied is given by the following equation (7):

σ(k)=σ(k+1)  (7)

Using the equations (1), (4), and (5), the duty ratio DUT(k) satisfyingthe equation (7) is determined by the equation (9) shown below. The dutyratio DUT(k) calculated with the equation (9) represents the equivalentcontrol input Ueq(k). The reaching law input Urch(k) and the adaptivelaw input Uadp(k) are defined by the respective equations (10) and (11)shown below. $\begin{matrix}\begin{matrix}{{{DUT}(k)} = \quad {\frac{1}{b1}\left\{ {{\left\lbrack {1 - {a1} - {VPOLE}} \right){{DTH}\left( {k + d} \right)}} +} \right.}} \\{\quad {{\left( {{VPOLE} - {a2}} \right){{DTH}\left( {k + d - 1} \right)}} - {c1} +}} \\{\quad {{{DTHR}\left( {k + d + 1} \right)} + {\left( {{VPOLE} - 1} \right){{DTHR}\left( {k + d} \right)}} -}} \\\left. \quad {{VPOLE} \times {{DTHR}\left( {k + d - 1} \right)}} \right\} \\{= \quad {{Ueq}(k)}}\end{matrix} & (9) \\{{{Urch}(k)} = {\frac{- F}{b1}\quad {\sigma \left( {k + d} \right)}}} & (10) \\{{{Uadp}(k)} = {\frac{- G}{b1}{\sum\limits_{i = 0}^{k + d}{\Delta \quad T\quad {\sigma (i)}}}}} & (11)\end{matrix}$

where F and G respectively represent a reaching law control gain and anadaptive law control gain, which are set as described below, and ΔTrepresents a control period.

Calculating the equation (9) requires a throttle valve opening deviationamount DTH(k+d) after the elapse of the dead time d and a correspondingtarget value DTHR(k+d+1). Therefore, the predicted deviation amountPREDTH(k) calculated by the state predictor 23 is used as the throttlevalve opening deviation amount DTH(k+d) after the elapse of the deadtime d, and the latest target value DTHR is used as the target valueDTHR(k+d+1).

Next, the reaching law control gain F and the adaptive law control gainG are determined so that the deviation state quantity can stably beplaced onto the switching straight line by the reaching law input Urchand the adaptive law input Uadp.

Specifically, a disturbance V(k) is assumed, and a stability conditionfor keeping the switching function value σ(k) stable against thedisturbance V(k) are determined to obtain a condition for setting thegains F and G. As a result, it has been obtained as the stabilitycondition that the combination of the gains F and G satisfies thefollowing equations (12) through (14), in other words, the combinationof the gains F and G should be located in a hatched region shown in FIG.5.

F>0  (12)

G>0  (13)

F<2−(ΔT/2)G  (14)

As described above, the equivalent control input Ueq(k), the reachinglaw input Urch(k), and the adaptive law input Uadp(k) are calculatedfrom the equations (9) through (11), and the duty ratio DUT(k) iscalculated as the sum of those inputs.

The model parameter identifier 22 calculates a model parameter vector ofthe controlled object model, based on the input (DUT(k)) and output(TH(k)) of the controlled object, as described above. Specifically, themodel parameter identifier 22 calculates a model parameter vector θ(k)according to a sequential identifying algorithm (generalized sequentialmethod-of-least-squares algorithm) represented by the following equation(15).

θ(k)=θ(k−1)+KP(k)ide(k)  (15)

θ(k)^(T) =[a 1′, a 2′, b 1′, c 1′]  (16)

where a1′, a2′, b1′, c1′ represent model parameters before a limitprocess described later is carried out, ide(k) represents an identifyingerror defined by the equations (17), (18), and (19) shown below, whereDTHHAT(k) represents an estimated value of the throttle valve openingdeviation amount DTH(k) (hereinafter referred to as “estimated throttlevalve opening deviation amount”) which is calculated using the latestmodel parameter vector θ(k−1), and KP(k) represents a gain coefficientvector defined by the equation (20) shown below. In the equation (20),P(k) represents a quartic square matrix calculated from the equation(21) shown below.

i d e (k)=DTH(k)−DTHHAT(k)  (17)

DTHHAT(k)=θ(k−1)^(T)ζ(k)  (18)

ζ(k)^(T) =[DTH(k−1), DTH(k−2), DUT(k−d−1), 1]  (19) $\begin{matrix}{{K\quad {P(k)}} = \frac{{P(k)}{\zeta (k)}}{1 + {{\zeta^{T}(k)}{P(k)}{\zeta (k)}}}} & (20) \\{{P\left( {k + 1} \right)} = {\frac{1}{\lambda_{1}}\left( {- \frac{\lambda_{2}{P(k)}{\zeta (k)}{\zeta^{T}(k)}}{\lambda_{1} + {\lambda_{2}{\zeta^{T}(k)}{P(k)}{\zeta (k)}}}} \right){P(k)}}} & (21) \\\left( {:{I\quad d\quad e\quad n\quad t\quad i\quad t\quad y\quad M\quad a\quad t\quad r\quad i\quad x}} \right) & \quad\end{matrix}$

In accordance with the setting of coefficients λ1 and λ2 in the equation(21), the identifying algorithm from the equations (15) through (21)becomes one of the following four identifying algorithm:

λ1 = 1, λ2 = 0 Fixed gain algorithm λ1 = 1, λ2 = 1Method-of-least-squares algorithm λ1 = 1, λ2 = λ Degressive gainalgorithm (λ is a given value other than 0, 1) λ1 = λ, λ2 = 1 WeightedMethod-of- least- squares algorithm (λ is a given value other than 0, 1)

In the present embodiment, it is required that the followingrequirements B1, B2, and B3 are satisfied:

B1) Adaptation to quasi-static dynamic characteristics changes andhardware characteristics variations

“Quasi-static dynamic characteristics changes” mean slow-ratecharacteristics changes such as power supply voltage fluctuations orhardware degradations due to aging.

B2) Adaptation to high-rate dynamic characteristics changes

Specifically, this means adaptation to dynamic characteristics changesdepending on changes in the throttle valve opening TH.

B3) Prevention of a drift of model parameters

The drift, which is an excessive increase of the absolute values ofmodel parameters, should be prevented. The drift of model parameters iscaused by the effect of the identifying error, which should not bereflected to the model parameters, due to nonlinear characteristics ofthe controlled object.

In order to satisfy the requirements B1 and B2, the coefficients λ1 andλ2 are set respectively to a given value λ and “0” so that the weightedMethod-of-least-squares algorithm is employed.

Next, the drift of model parameters will be described below. As shown inFIG. 6A and FIG. 6B, if a residual identifying error, which is caused bynonlinear characteristics such as friction characteristics of thethrottle valve, exists after the model parameters have been converged toa certain extent, or if a disturbance whose average value is not zero issteadily applied, then residual identifying errors are accumulated,causing a drift of model parameters.

Since such a residual identifying error should not be reflected to thevalues of model parameters, a dead zone process is carried out using adead zone function Fn1 as shown in FIG. 7A. Specifically, a correctedidentifying error idenl(k) is calculated from the following equation(23), and a model parameter vector θ(k) is calculated using thecorrected identifying error idenl(k). That is, the following equation(15a) is used instead of the above equation (15). In this manner, therequirement B3) can be satisfied.

idenl(k)=Fnl(ide(k))  (23)

θ(k)=θ(k−1)+KP(k)idenl(k)  (15a)

The dead zone function Fn1 is not limited to the function shown in FIG.7A. A discontinuous dead zone function as shown in FIG. 7B or anincomplete dead zone function as shown in FIG. 7C may be used as thedead zone function Fnl. However, it is impossible to completely preventthe drift if the incomplete dead zone function is used.

The amplitude of the residual identifying error changes according to anamount of change in the throttle valve opening TH. In the presentembodiment, a dead zone width parameter EIDNRLMT which defines the widthof the dead zone shown in FIGS. 7A through 7C is set according to thesquare average value DDTHRSQA of an amount of change in the targetthrottle valve opening THR. Specifically, the dead zone width parameterEIDNRLMT is set such that it increases as the square average valueDDTHRSQA increases. According to such setting of the dead zone widthparameter EIDNRLMT, it is prevented to neglect an identifying error tobe reflected to the values of the model parameters as the residualidentifying error. In the following equation (24), DDTHR represents anamount of change in the target throttle valve opening THR, which iscalculated from the following equation (25): $\begin{matrix}{{D\quad D\quad T\quad H\quad R\quad S\quad Q\quad {A(k)}} = {\frac{1}{n + 1}{\sum\limits_{i = 0}^{n}{D\quad D\quad T\quad H\quad {R(i)}^{2}}}}} & (24) \\{\begin{matrix}{{D\quad D\quad T\quad H\quad {R(k)}} = {{D\quad T\quad H\quad {R(k)}} - {D\quad T\quad H\quad {R\left( {k - 1} \right)}}}} \\{= {{T\quad H\quad {R(k)}} - {T\quad H\quad {R\left( {k - 1} \right)}}}}\end{matrix}} & (25)\end{matrix}$

Since the throttle valve opening deviation amount DTH is controlled tothe target value DTHR by the adaptive sliding mode controller 21, thetarget value DTHR in the equation (25) may be changed to the throttlevalve opening deviation amount DTH. In this case, an amount of changeDDTH in the throttle valve opening deviation amount DTH may becalculated, and the dead zone width parameter EIDNRLMT may be setaccording to the square average value DDTHRSQA obtained by replacingDDTHR in the equation (24) with DDTH.

For further improving the robustness of the control system, it iseffective to further stabilize the adaptive sliding mode controller 21.In the present embodiment, the elements a1′, a2′, b1′, and c1′ of themodel parameter vector θ(k) calculated from the equation (15) aresubjected to the limit process so that a corrected model parametervector θL(k)(θL(k)^(T)=[a1, a2, b1, c1]) is calculated. The adaptivesliding mode controller 21 performs a sliding mode control using thecorrected model parameter vector θL(k). The limit process will bedescribed later in detail referring to the flowcharts.

Next, a method for calculating the predicted deviation amount PREDTH inthe state predictor 23 will be described below.

First, matrixes A, B and vectors X(k), U(k) are defined according to thefollowing equations (26) through (29). $\begin{matrix}{A = \begin{bmatrix}{a1} & {a2} \\1 & 0\end{bmatrix}} & (26) \\{B = \begin{bmatrix}{b1} & {c1} \\0 & 0\end{bmatrix}} & (27) \\{{X(k)} = \begin{bmatrix}{D\quad T\quad {H(k)}} \\{D\quad T\quad {H\left( {k - 1} \right)}}\end{bmatrix}} & (28) \\{{U(k)} = \begin{bmatrix}{D\quad U\quad {T(k)}} \\1\end{bmatrix}} & (29)\end{matrix}$

By rewriting the equation (1) which defines the controlled object model,using the matrixes A, B and the vectors X(k), U(k), the followingequation (30) is obtained.

X(k+1)=AX(k)+BU(k−d)  (30)

Determining X(k+d) from the equation (30), the following equation (31)is obtained. $\begin{matrix}{{X\left( {k + d} \right)} = {{A^{d}{X(k)}} + \left\lbrack \begin{matrix}{A^{d - 1}B} & {A^{d - 2}B} & \ldots & {A\quad B} & {\left. B \right\rbrack \quad\begin{bmatrix}{U\left( {k - 1} \right)} \\{U\left( {k - 2} \right)} \\\vdots \\{U\left( {k - d} \right)}\end{bmatrix}}\end{matrix} \right.}} & (31)\end{matrix}$

If matrixes A′ and B′ are defined by the following equations (32), (33),using the model parameters a1′, a2′, b1′, and c1′ which are notsubjected to the limit process, a predicted vector XHAT(k+d) is given bythe following equation (34). $\begin{matrix}{A^{\prime} = \begin{bmatrix}{a1}^{\prime} & {a2}^{\prime} \\1 & 0\end{bmatrix}} & (32) \\{B^{\prime} = \begin{bmatrix}{b1}^{\prime} & {c1}^{\prime} \\0 & 0\end{bmatrix}} & (33)\end{matrix}$

$\begin{matrix}{{X\quad H\quad A\quad {T\left( {k + d} \right)}} = {{{A^{\prime}}^{d}{X(k)}} + \left\lbrack \begin{matrix}{A^{{\prime \quad d} - 1}B^{\prime}} & {A^{{\prime \quad d} - 2}B^{\prime}} & \ldots & {A^{\prime}\quad B^{\prime}} & {\left. B^{\prime} \right\rbrack \quad\begin{bmatrix}{U\left( {k - 1} \right)} \\{U\left( {k - 2} \right)} \\\vdots \\{U\left( {k - d} \right)}\end{bmatrix}}\end{matrix} \right.}} & (34)\end{matrix}$

The first-row element DTHHAT(k+d) of the predicted vector XHAT(k+d)corresponds to the predicted deviation amount PREDTH(k), and is given bythe following equation (35). $\begin{matrix}\begin{matrix}{{{PREDTH}(k)} = \quad {{DTHHAT}\left( {k + d} \right)}} \\{= \quad {{{\alpha 1} \times {{DTH}(k)}} + {{\alpha 2} \times {{DTH}\left( {k - 1} \right)}} +}} \\{\quad {{\beta \quad 1 \times {{DUT}\left( {k - 1} \right)}} + {\beta \quad 2 \times {{DUT}\left( {k - 2} \right)}} + \ldots +}} \\{\quad {{\beta \quad d \times {{DUT}\left( {k - d} \right)}} + {\gamma \quad 1} + {\gamma \quad 2} + \ldots + {\gamma \quad d}}}\end{matrix} & (35)\end{matrix}$

where α1 represents a first-row, first-column element of the matrixA′^(d), α2 represents a first-row, second-column element of the matrixA′^(d), βi represents a first-row, first-column element of the matrixA′^(d−i)B′, and γi represents a first-row, second-column element of thematrix A′^(d−i)B′.

By applying the predicted deviation amount PREDTH(k) calculated from theequation (35) to the equation (9), and replacing the target valuesDTHR(k+d+1), DTHR(k+d), and DTHR(k+d−1) respectively with DTHR(k),DTHR(k−1), and DTHR(k−2), the following equation (9a) is obtained. Fromthe equation (9a), the equivalent control input Ueq(k) is calculated.$\begin{matrix}{\begin{matrix}{{D\quad U\quad {T(k)}} = \quad {\frac{1}{b1}\left\{ {{\left( {1 - {a1} - {V\quad P\quad O\quad L\quad E}} \right)P\quad R\quad E\quad D\quad T\quad {H(k)}} +} \right.}} \\{\quad {{\left( {{V\quad P\quad O\quad L\quad E} - {a2}} \right)P\quad R\quad E\quad D\quad T\quad {H\left( {k - 1} \right)}} - {c1} +}} \\{\quad {{D\quad T\quad H\quad {R(k)}} + {\left( {{V\quad P\quad O\quad L\quad E} - 1} \right)D\quad T\quad H\quad {R\left( {k - 1} \right)}} -}} \\{\quad \left. {V\quad P\quad O\quad L\quad E \times D\quad T\quad H\quad {R\left( {k - 2} \right)}} \right\}} \\{= \quad {U\quad e\quad {q(k)}}}\end{matrix}} & \left( \text{9a} \right)\end{matrix}$

Using the predicted deviation amount PREDTH(k) calculated from theequation (35), a predicted switching function value σpre(k) is definedby the following equation (36). The reaching law input Urch(k) and theadaptive law input Uadp(k) are calculated respectively from thefollowing equations (10a) and (11a).

σpre(k)=(PREDTH(k)−DTHR(k−1))+VPOLE(PREDTH(k−1)−DTHR(k−2))  (36)$\begin{matrix}{{U\quad r\quad c\quad {h(k)}} = {\frac{- F}{b1}\sigma \quad p\quad r\quad {e(k)}}} & \left( \text{10a} \right) \\{{U\quad a\quad d\quad {p(k)}} = {\frac{- G}{b1}{\sum\limits_{i = 0}^{k}{\Delta \quad T\quad \sigma \quad p\quad r\quad {e(i)}}}}} & \left( \text{11a} \right)\end{matrix}$

The model parameter c1′ is a parameter representing a deviation of thedefault opening THDEF and disturbance. Therefore, as shown in FIG. 8,the model parameter c1′ changes with disturbance, but can be regarded assubstantially constant in a relatively short period. In the presentembodiment, the model parameter c1′ is statistically processed, and thecentral value of its variations is calculated as a default openingdeviation thdefadp. The default opening deviation thdefadp is used forcalculating the throttle valve opening deviation amount DTH and thetarget value DTHR.

Generally, the method of least squares is known as a method of thestatistic process. In the statistic process according to the method ofleast squares, all data, i.e., all identified parameters c1′, obtainedin a certain period are stored in a memory and the stored data issubjected to a batch calculation of the statistic process at a certaintiming. However, the batch calculation requires a memory having a largestorage capacity for storing all data, and an increased amount ofcalculations are necessary because inverse matrix calculations arerequired.

Therefore, according to the present embodiment, the sequentialmethod-of-least-squares algorithm for adaptive control which isindicated by the equations (15) through (21) is applied to the statisticprocess, and the central value of the least squares of the modelparameter c1 is calculated as the default opening deviation thdefadp.

Specifically, in the equations (15) through (21), by replacing θ(k) andθ(k)^(T) with thdefadp, replacing ζ(k) and ζ(k)^(T) with “1”, replacingide(k) with ecl(k), replacing KP(k) with KPTH(k), replacing P(k) withPTH(k), and replacing λ1 and λ2 respectively with λ1′ and λ2′, thefollowing equations (37) through (40) are obtained.

thdefadp(k+1)=thdefadp(k)+KPTH(k)ec1(k)  (37) $\begin{matrix}{{K\quad P\quad T\quad {H(k)}} = \frac{P\quad T\quad {H(k)}}{1 + {P\quad T\quad {H(k)}}}} & (38) \\{{P\quad T\quad {H\left( {k + 1} \right)}} = {\frac{1}{\lambda_{1}^{\prime}}\left( {1 - \frac{\lambda_{2}^{\prime}P\quad T\quad {H(k)}}{\lambda_{1}^{\prime} + {\lambda_{2}^{\prime}P\quad T\quad {H(k)}}}} \right)P\quad T\quad {H(k)}}} & (39)\end{matrix}$

 ec 1(k)=c1′(k)−thdefadp(k)  (40)

One of the four algorithms described above can be selected according tothe setting of the coefficients λ1′ and λ2′. In the equation (39), thecoefficient λ1′ is set to a given value other than 0 or 1, and thecoefficient λ2′ is set to 1, thus employing the weighted method of leastsquares.

For the calculations of the equations (37) through (40), the values tobe stored are thdefadp(k+1) and PTh(k+1) only, and no inverse matrixcalculations are required. Therefore, by employing the sequentialmethod-of-least-squares algorithm, the model parameter c1 can bestatistically processed according to the method of least squares whileovercoming the shortcomings of a general method of least squares.

The default opening deviation thdefadp obtained as a result of thestatistic process is applied to the equations (2) and (3), and thethrottle valve opening deviation amount DTH(k) and the target valueDTHR(k) are calculated from the following equations (41) and (42)instead of the equations (2) and (3).

DTH(k)=TH(k)−THDEF+thdefadp  (41)

DTHR(k)=THR(k)−THDEF+thdefadp  (42)

Using the equations (41) and (42), even when the default opening THDEFis shifted from its designed value due to characteristic variations oraging of the hardware, the shift can be compensated to perform anaccurate control process.

Operation processes executed by the CPU in the ECU 7 for realizing thefunctions of the adaptive sliding mode controller 21, the modelparameter identifier 22, and the state predictor 23 will be describedbelow.

FIG. 9 is a flowchart showing a process of the throttle valve openingcontrol. The process is executed by the CPU in the ECU 7 in everypredetermined period of time (e.g., 2 msec).

In step S11, a process of setting a state variable shown in FIG. 10 isperformed. Calculations of the equations (41) and (42) are executed todetermine the throttle valve opening deviation amount DTH(k) and thetarget value DTHR(k) (steps S21 and S22 in FIG. 10). The symbol (k)representing a current value may sometimes be omitted as shown in FIG.10.

In step S12, a process of performing calculations of the model parameteridentifier as shown in FIG. 11, i.e., a process of calculating the modelparameter vector θ(k) from the equation (15a), is carried out. Further,the model parameter vector θ(k) is subjected to the limit process sothat the corrected model parameter vector θL(k) is calculated.

In step S13, a process of performing calculations of the state predictoras shown in FIG. 21 is carried out to calculate the predicted deviationamount PREDTH(k).

Next, using the corrected model parameter vector θL(k) calculated instep S12, a process of calculating the control input Usl(k) as shown inFIG. 22 is carried out in step S14. Specifically, the equivalent controlinput Ueq, the reaching law input Urch(k), and the adaptive law inputUadp(k) are calculated, and the control input Usl(k) (=duty ratioDUT(k)) is calculated as a sum of these inputs Ueq(k), Urch(k), andUadp(k).

In step S16, a process of stability determination of the sliding modecontroller as shown in FIG. 29 is carried out. Specifically, thestability is determined based on a differential value of the Lyapunovfunction, and a stability determination flag FSMCSTAB is set. When thestability determination flag FSMCSTAB is set to “1”, this indicates thatthe adaptive sliding mode controller 21 is unstable.

If the stability determination flag FSMCSTAB is set to “1”, indicatingthat the adaptive sliding mode controller 21 is unstable, the switchingfunction setting parameter VPOLE is set to a predetermined stabilizingvalue XPOLESTB (see steps S231 and S232 in FIG. 24), and the equivalentcontrol input Ueq is set to “0”. That is, the control process by theadaptive sliding mode controller 21 is switched to a control processbased on only the reaching law input Urch and the adaptive law inputUadp, to thereby stabilize the control (see steps S206 and S208 in FIG.22).

Further, when the adaptive sliding mode controller 21 has becomeunstable, the equations for calculating the reaching law input Urch andthe adaptive law input Uadp are changed. Specifically, the values of thereaching law control gain F and the adaptive law control gain G arechanged to values for stabilizing the adaptive sliding mode controller21, and the reaching law input Urch and the adaptive law input Uadp arecalculated without using the model parameter b1 (see FIGS. 27 and 28).According to the above stabilizing process, it is possible to quicklyterminate the unstable state of the adaptive sliding mode controller 21,and to bring the adaptive sliding mode controller 21 back to its stablestate.

In step S17, a process of calculating the default opening deviationthdefadp as shown in FIG. 30 is performed to calculate the defaultopening deviation thdefadp.

FIG. 11 is a flowchart showing a process of performing calculations ofthe model parameter identifier 22.

In step S31, the gain coefficient vector KP(k) is calculated from theequation (20). Then, the estimated throttle valve opening deviationamount DTHHAT(k) is calculated from the equation (18) in step S32. Instep S33, a process of calculating the identifying error idenl(k) asshown in FIG. 12 is carried out. The estimated throttle valve openingdeviation amount DTHHAT(k) calculated in step S32 is applied to theequation (17) to calculate the identifying error ide(k). Further in stepS32, the dead zone process using the function shown in FIG. 7A iscarried out to calculate the corrected identifying error idenl.

In step S34, the model parameter vector θ(k) is calculated from theequation (15a). Then, the model parameter vector θ(k) is subjected tothe stabilization process in step S35. That is, each of the modelparameters is subjected to the limit process to calculate the correctedmodel parameter vector θL(k).

FIG. 12 is a flowchart showing a process of calculating the identifyingerror idenl(k) which is carried out in step S33 shown in FIG. 11.

In step S51, the identifying error ide(k) is calculated from theequation (17). Then, it is determined whether or not the value of acounter CNTIDST which is incremented in step S53 is greater than apredetermined value XCNTIDST that is set according to the dead time d ofthe controlled object (step S52). The predetermined value XCNTIDST isset, for example, to “3” according to a dead time d=2. Since the counterCNTIDST has an initial value of “0”, the process first goes to step S53,in which the counter CNTIDST is incremented by “1”. Then, theidentifying error ide(k) is set to “0” in step S54, after which theprocess goes to step S55. Immediately after starting identifying themodel parameter vector θ(k), no correct identifying error can beobtained by the equation (17). Therefore, the identifying error ide(k)is set to “0” according to steps S52 through S54, instead of using thecalculated result of the equation (17).

If the answer to the step S52 is affirmative (YES), then the processimmediately proceeds to step S55.

In step S55, the identifying error ide(k) is subjected to a low-passfiltering. Specifically, when identifying the model parameters of ancontrolled object which has low-pass characteristics, the identifyingweight of the method-of-least-squares algorithm for the identifyingerror ide(k) has frequency characteristics as indicated by the solidline L1 in FIG. 13A. By the low-pass filtering of the identifying erroride(k), the frequency characteristics as indicated by the solid line L1is changed to a frequency characteristics as indicated by the brokenline L2 where the high-frequency components are attenuated. The reasonfor executing the low-pass filtering will be described below.

The frequency characteristics of the actual controlled object havinglow-pass characteristics and the controlled object model thereof arerepresented respectively by the solid lines L3 and L4 in FIG. 13B.Specifically, if the model parameters are identified by the modelparameter identifier 22 with respect to the controlled object which haslow-pass characteristics (characteristics of attenuating high-frequencycomponents), the identified model parameters are largely affected by thehigh-frequency-rejection characteristics so that the gain of thecontrolled object model becomes lower than the actual characteristics ina low-frequency range. As a result, the sliding mode controller 21excessively corrects the control input.

By changing the frequency characteristics of the weighting of theidentifying algorithm to the characteristics indicated by the brokenline L2 in FIG. 13A according to the low-pass filtering, the frequencycharacteristics of the controlled object are changed to frequencycharacteristics indicated by the broken line L5 in FIG. 13B. As aresult, the frequency characteristics of the controlled object model ismade to coincide with the actual frequency characteristics, or the lowfrequency gain of the controlled object model is corrected to a levelwhich is slightly higher than the actual gain. Accordinly, it ispossible to prevent the control input from being excessively correctedby the sliding mode controller 21, to thereby improve the robustness ofthe control system and further stabilize the control system.

The low-pass filtering is carried out by storing past values ide(k−i) ofthe identifying error (e.g., 10 past values for i=1 through 10) in aring buffer, multiplying the past values by weighting coefficients, andadding the products of the past values and the weighting coefficients.

Since the identifying error ide(k) is calculated from the equations(17), (18), and (19), the same effect as described above can be obtainedby performing the same low-pass filtering on the throttle valve openingdeviation amount DTH(k) and the estimated throttle valve openingdeviation amount DTHHAT(k), or by performing the same low-pass filteringon the throttle valve opening deviation amounts DTH(k−1), DTH(k−2) andthe duty ratio DUT(k−d−1).

Referring back to FIG. 12, the dead zone process as shown in FIG. 14 iscarried out in step S56. In step S61 shown in FIG. 14, “n” in theequation (24) is set, for example, to “5” to calculate the squareaverage value DDTHRSQA of an amount of change of the target throttlevalve opening THR. Then, an EIDNRLMT table shown in FIG. 15 is retrievedaccording to the square average value DDTHRSQA to calculate the deadzone width parameter EIDNRLMT (step S62).

In step S63, it is determined whether or not the identifying erroride(k) is greater than the dead zone width parameter EIDNRLMT. If ide(k)is greater than EIDNRLMT, the corrected identifying error idenl(k) iscalculated from the following equation (43) in step S67.

idenl(k)=ide(k)−EIDNRLMT  (43)

If the answer to step S63 is negative (NO), it is determined whether ornot the identifying error ide(k) is greater than the negative value ofthe dead zone width parameter EIDNRLMT with a minus sign (step S64).

If ide(k) is less than −EIDNRLMT, the corrected identifying erroridenl(k) is calculated from the following equation (44) in step S65.

idenl(k)=ide(k)+EIDNRLMT  (44)

If the identifying error ide(k) is in the range between +EIDNRLMT and−EIDNRLMT, the corrected identifying error idenl(k) is set to “0” instep S66.

FIG. 16 is a flowchart showing a process of stabilizing the modelparameter vector θ(k), which is carried out in step S35 shown in FIG.11.

In step S71 shown in FIG. 16, flags FA1STAB, FA2STAB, FB1LMT, and FC1LMTused in this process are initialized to be set to “0”. In step S72, thelimit process of the model parameters a1′ and a2′ shown in FIG. 17 isexecuted. In step S73, the limit process of the model parameter b1′shown in FIG. 19 is executed. In step S74, the limit process of themodel parameter c1′ shown in FIG. 20 is executed.

FIG. 17 is a flowchart showing the limit process of the model parametersa1′ and a2′, which is carried out in the step S72 shown in FIG. 16. FIG.18 is a diagram illustrative of the process shown in FIG. 17, and willbe referred to with FIG. 17.

In FIG. 18, combinations of the model parameters a1′ and a2′ which arerequired to be limited are indicated by “x” symbols, and the range ofcombinations of the model parameters a1′ and a2′ which are stable areindicated by a hatched region (hereinafter referred to as “stableregion”). The limit process shown in FIG. 17 is a process of moving thecombinations of the model parameters a1′ and a2′ which are in theoutside of the stable region into the stable region at positionsindicated by “◯” symbols.

In step S81, it is determined whether or not the model parameter a2′ isgreater than or equal to a predetermined a2 lower limit value XIDA2L.The predetermined a2 lower limit value XIDA2L is set to a negative valuegreater than “−1”. Stable corrected model parameters a1 and a2 areobtained when setting the predetermined a2 lower limit value XIDA2L to“−1”. However, the predetermined a2 lower limit value XIDA2L is set to anegative value greater than “−1” because the matrix A defined by theequation (26) to the “n”th power may occasionally become unstable (whichmeans that the model parameters a1′ and a2′ do not diverge, butoscillate).

If a2′ is less than XIDA2L in step S81, the corrected model parameter a2is set to the lower limit value XIDA2L, and an a2 stabilizing flagFA2STAB is set to “1”. When the a2 stabilizing flag FA2STAB is set to“1”, this indicates that the corrected model parameter a2 is set to thelower limit value XIDA2L. In FIG. 18, the correction of the modelparameter in a limit process P1 of steps S81 and S82 is indicated by thearrow lines with “P1”.

If the answer to the step S81 is affirmative (YES), i.e., if a2′ isgreater than or equal to XIDA2L, the corrected model parameter a2 is setto the model parameter a2′ in step S83.

In steps S84 and S85, it is determined whether or not the modelparameter a1′ is in a range defined by a predetermined a1 lower limitvalue XIDA1L and a predetermined al upper limit value XIDA1H. Thepredetermined al lower limit value XIDA1L is set to a value which isequal to or greater than “−2” and lower than “0”, and the predetermineda1 upper limit value XIDA1H is set to “2”, for example.

If the answers to steps S84 and S85 are affirmative (YES), i.e., if a1′is greater than or equal to XIDA1L and less than or equal to XIDA1H, thecorrected model parameter a1 is set to the model parameter a1′ in stepS88.

If a1′ is less than XIDA1L in step S84, the corrected model parameter a1is set to the lower limit value XIDA1L and an a1 stabilizing flagFA1STAB is set to “1” in step S86. If a1′ is greater than XIDA1H in stepS85, the corrected model parameter a1 is set to the upper limit valueXIDA1H and the a1 stabilizing flag FA1STAB is set to “1” in step S87.When the a1 stabilizing flag FA1STAB is set to “1”, this indicates thatthe corrected model parameter a1 is set to the lower limit value XIDA1Lor the upper limit value XIDA1H. In FIG. 18, the correction of the modelparameter in a limit process P2 of steps S84 through S87 is indicated bythe arrow lines with “P2”.

In step S90, it is determined whether or not the sum of the absolutevalue of the corrected model parameter a1 and the corrected modelparameter a2 is less than or equal to a predetermined stabilitydetermination value XA2STAB. The predetermined stability determinationvalue XA2STAB is set to a value close to “1” but less than “1” (e.g.,“0.99”).

Straight lines L1 and L2 shown in FIG. 18 satisfy the following equation(45).

a 2+|a 1|=XA 2 STAB  (45)

Therefore, in step S90, it is determined whether or not the combinationof the corrected model parameters a1 and a2 is placed at a position onor lower than the straight lines L1 and L2 shown in FIG. 18. If theanswer to step S90 is affirmative (YES), the limit process immediatelyends, since the combination of the corrected model parameters a1 and a2is in the stable region shown in FIG. 18.

If the answer to step S90 is negative (NO), it is determined whether ornot the corrected model parameter a1 is less than or equal to a valueobtained by subtracting the predetermined a2 lower limit value XIDA2Lfrom the predetermined stability determination value XA2STAB in step S91(since XIDA2L is less than “0”, XA2STAB−XIDA2L is greater than XA2STAB).If the corrected model parameter a1 is equal to or less than(XA2STAB−XIDA2L), the corrected model parameter a2 is set to(XA2STAB−|a1|) and the a2 stabilizing flag FA2STAB is set to “1” in stepS92.

If the corrected model parameter a1 is greater than (XA2STAB−XIDA2L) instep S91, the corrected model parameter a1 is set to (XA2STAB−XIDA2L) instep S93. Further in step S93, the corrected model parameter a2 is setto the predetermined a2 lower limit value XIDA2L, and the a1 stabilizingflag FA1STAB and the a2 stabilizing flag FA2STAB are set to “1” in stepS93.

In FIG. 18, the correction of the model parameter in a limit process P3of steps S91 and S92 is indicated by the arrow lines with “P3”, and thecorrection of the model parameter in a limit processP4 in steps S91 andS93 is indicated by the arrow lines with “P4”.

As described above, the limit process shown in FIG. 17 is carried out tobring the model parameters a1′ and a2′ into the stable region shown inFIG. 18, thus calculating the corrected model parameters a1 and a2.

FIG. 19 is a flowchart showing a limit process of the model parameterb1′, which is carried out in step S73 shown in FIG. 16.

In steps S101 and S102, it is determined whether or not the modelparameter b1′ is in a range defined by a predetermined b1 lower limitvalue XIDB1L and a predetermined b1 upper limit value XIDB1H. Thepredetermined b1 lower limit value XIDB1L is set to a positive value(e.g., “0.1”), and the predetermined b1 upper limit value XIDB1H is setto “1”, for example.

If the answers to steps S101 and S102 are affirmative (YES), i.e., ifb1′ is greater than or equal to XIDB1L and less than or equal to XIDB1H,the corrected model parameter b1 is set to the model parameter b1′ instep S105.

If b1′ is less than XIDB1L in step S101, the corrected model parameterb1 is set to the lower limit value XIDB1L, and a b1 limiting flag FB1LMTis set to “1” in step S104. If b1′ is greater than XIDB1H in step S102,then the corrected model parameter b1 is set to the upper limit valueXIDB1H, and the b1 limiting flag FB1LMT is set to “1” in step S103. Whenthe b1 limiting flag FB1LMT is set to “1”, this indicates that thecorrected model parameter b1 is set to the lower limit value XIDB1L orthe upper limit value XIDB1H.

FIG. 20 is a flowchart showing a limit process of the model parameterc1′, which is carried out in step S74 shown in FIG. 16.

In steps S111 and S112, it is determined whether or not the modelparameters c1′ is in a range defined by a predetermined c1 lower limitvalue XIDC1L and a predetermined c1 upper limit value XIDC1H. Thepredetermined c1 lower limit value XIDC1L is set to “−60”, for example,and the predetermined c1 upper limit value XIDC1H is set to “60”, forexample.

If the answers to steps S111 and S112 are affirmative (YES), i.e., ifc1′ is greater than or equal to XIDC1L and less than or equal to XIDC1H,the corrected model parameter c1 is set to the model parameter c1′ instep S115.

If c1′ is less than XIDC1L in step S111, the corrected model parameterc1 is set to the lower limit value XIDC1L, and a c1 limiting flag FC1LMTis set to “1” in step S114. If c1′ is greater than XIDC1H in step S112,the corrected model parameter c1 is set to the upper limit value XIDC1H,and the c1 limiting flag FC1LMT is set to “1” in step S113. When the c1limiting flag FC1LMT is set to “1”, this indicates that the correctedmodel parameter c1 is set to the lower limit value XIDC1L or the upperlimit value XIDC1H.

FIG. 21 is a flowchart showing a process of calculations of the statepredictor, which is carried out in step S13 shown in FIG. 9.

In step S121, the matrix calculations are executed to calculate thematrix elements α1, α2, β1, β2, γ1 through γd in the equation (35).

In step S122, the predicted deviation amount PREDTH(k) is calculatedfrom the equation (35).

FIG. 22 is a flowchart showing a process of calculation of the controlinput Usl (=DUT) applied to the throttle valve actuating device 10,which is carried out in step S14 shown in FIG. 9.

In step S201, a process of calculation of the predicted switchingfunction value σpre, which is shown in FIG. 23, is executed. In stepS202, a process of calculation of the integrated value of the predictedswitching function value σpre, which is shown in FIG. 26, is executed.In step S203, the equivalent control input Ueq is calculated from theequation (9). In step S204, a process of calculation of the reaching lawinput Urch, which is shown in FIG. 27, is executed. In step S205, aprocess of calculation of the adaptive law input Uadp, which is shown inFIG. 28, is executed.

In step S206, it is determined whether or not the stabilitydetermination flag FSMCSTAB set in the process shown in FIG. 29 is “1”.When the stability determination flag FSMCSTAB is set to “1”, thisindicates that the adaptive sliding mode controller 21 is unstable.

If FSMCSTAB is “0” in step S206, indicating that the adaptive slidingmode controller 21 is stable, the control inputs Ueq, Urch, and Uadpwhich are calculated in steps S203 through S205 are added, therebycalculating the control input Usl in step S207.

If FSMCSTAB is “1” in step S206, indicating that the adaptive slidingmode controller 21 is unstable, the sum of the reaching law input Urchand the adaptive law input Uadp is calculated as the control input Usl.In other words, the equivalent control input Ueq is not used forcalculating the control input Usl, thus preventing the control systemfrom becoming unstable.

In steps S209 and S210, it is determined whether or not the calculatedcontrol input Usl is in a range defined between a predetermined upperlimit value XUSLH and a predetermined lower limit value XUSLL. If thecontrol input Usl is in the range between XUSLH and XUSLL, the processimmediately ends. If the control input Usl is less than or equal to thepredetermined lower limit value XUSLL in step S209, the control inputUsl is set to the predetermined lower limit value XUSLL in step S212. Ifthe control input Usl is greater than or equal to the predeterminedupper limit value XUSLH in step S210, the control input Usl is set tothe predetermined upper limit value XUSLH in step S211.

FIG. 23 is a flowchart showing a process of calculating the predictedswitching function value σpre, which is carried out in step S201 shownin FIG. 22.

In step S221, the process of calculating the switching function settingparameter VPOLE, which is shown in FIG. 24 is executed. Then, thepredicted switching function value σpre(k) is calculated from theequation (36) in step S222.

In steps S223 and S224, it is determined whether or not the calculatedpredicted switching function value σpre(k) is in a range defined betweena predetermined upper value XSGMH and a predetermined lower limit valueXSGML. If the calculated predicted switching function value σpre(k) isin the range between XSGMH and XSGML, the process shown in FIG. 23immediately ends. If the calculated predicted switching function valueσpre(k) is less than or equal to the predetermined lower limit valueXSGML in step S223, the calculated predicted switching function valueσpre(k) is set to the predetermined lower limit value XSGML in stepS225. If the calculated predicted switching function value σpre(k) isgreater than or equal to the predetermined upper limit value XSGMH instep S224, the calculated predicted switching function value σpre(k) isset to the predetermined upper limit value XSGMH in step S226.

FIG. 24 is a flowchart showing a process of calculating the switchingfunction setting parameter VPOLE, which is carried out in step S221shown in FIG. 23.

In step S231, it is determined whether or not the stabilitydetermination flag FSMCSTAB is “1”. If FSMCSTAB is “1” in step S231,indicating that the adaptive sliding mode controller 21 is unstable, theswitching function setting parameter VPOLE is set to a predeterminedstabilizing value XPOLESTB in step S232. The predetermined stabilizingvalue XPOLESTB is set to a value which is greater than “−1” but veryclose to “−1” (e.g., “−0.999”).

If FSMCSTAB is “0”, indicating that the adaptive sliding mode controller21 is stable, an amount of change DDTHR(k) in the target value DTHR(k)is calculated from the following equation (46) in step S233.

DDTHR(k)=DTHR(k)−DTHR(k−1)  (46)

In step S234, a VPOLE map is retrieved according to the throttle valveopening deviation amount DTH and the amount of change DDTHR calculatedin step S233 to calculate the switching function setting parameterVPOLE. As shown in FIG. 25A, the VPOLE map is set so that the switchingfunction setting parameter VPOLE increases when the throttle valveopening deviation amount DTH has a value in the vicinity of “0”, i.e.,when the throttle valve opening TH is in the vicinity of the defaultopening THDEF, and the switching function setting parameter VPOLE has asubstantially constant value regardless of changes of the throttle valveopening deviation amount DTH, when the throttle valve opening deviationamount DTH has values which are not in the vicinity of “0”. The VPOLEmap is also set so that the switching function setting parameter VPOLEincreases as the amount of change DDTHR in target value increases asindicated by the solid line in FIG. 25B, and the switching functionsetting parameter VPOLE increases as the amount of change DDTHR in thetarget value has a value in the vicinity of “0” as indicated by thebroken line in FIG. 25B, when the throttle valve opening deviationamount DTH has a value in the vicinity of “0”.

Specifically, when the target value DTHR for the throttle valve openingchanges greatly in the decreasing direction, the switching functionsetting parameter VPOLE is set to a relatively small value. This makesit possible to prevent the throttle valve 3 from colliding with thestopper for stopping the throttle valve 3 in the fully closed position.In the vicinity of the default opening THDEF, the switching functionsetting parameter VPOLE is set to a relatively large value, whichimproves the controllability in the vicinity of the default openingTHDEF.

As shown in FIG. 25C, the VPOLE map may be set so that the switchingfunction setting parameter VPOLE decreases when the throttle valveopening TH is in the vicinity of the fully closed opening or the fullyopen opening. Therefore, when the throttle valve opening TH is in thevicinity of the fully closed opening or the fully open opening, thespeed for the throttle valve opening TH to follow up the target openingTHR is reduced. As a result, collision of the throttle valve 3 with thestopper can more positively be avoided (the stopper also stops thethrottle valve 3 in the fully open position).

In steps S235 and S236, it is determined whether or not the calculatedswitching function setting parameter VPOLE is in a range defined betweena predetermined upper limit value XPOLEH and a predetermined lower limitXPOLEL. If the switching function setting parameter VPOLE is in therange between XPOLEH and XPOLEL, the process shown immediately ends. Ifthe switching function setting parameter VPOLE is less than or equal tothe predetermined lower limit value XPOLEL in step S236, the switchingfunction setting parameter VPOLE is set to the predetermined lower limitvalue XPOLEL in step S238. If the switching function setting parameterVPOLE is greater than or equal to the predetermined upper limit valueXPOLEH in step S235, the switching function setting parameter VPOLE isset to the predetermined upper limit value XPOLEH in step S237.

FIG. 26 is a flowchart showing a process of calculating an integratedvalue of σpre, SUMSIGMA, of the predicted switching function value σpre.This process is carried out in step S202 shown in FIG. 22. Theintegrated value SUMSIGMA is used for calculating the adaptive law inputUadp in the process shown in FIG. 28 which will be described later (seethe equation (11a)).

In step S241, the integrated value SUMSIGMA is calculated from thefollowing equation (47) where ΔT represents a calculation period.

SUMSIGMA(k)=SUMSIGMA(k−1)+σpre×ΔT  (47)

In steps S242 and S243, it is determined whether or not the calculatedintegrated value SUMSIGMA is in a range defined between a predeterminedupper limit value XSUMSH and a predetermined lower limit value XSUMSL.If the integrated value SUMSIGMA is in the range between XSUMSH andXSUMSL, the process immediately ends. If the integrated value SUMSIGMAis less than or equal to the predetermined lower limit value XSUMSL instep S242, the integrated value SUMSIGMA is set to the predeterminedlower limit value XSUMSL in step S244. If the integrated value SUMSIGMAis greater than or equal to the predetermined upper limit value XSUMSHin step S243, the integrated value SUMSIGMA is set to the predeterminedupper limit value XSUMSH in step S245.

FIG. 27 is a flowchart showing a process of calculating the reaching lawinput Urch, which is carried out in step S204 shown in FIG. 22.

In step S261, it is determined whether or not the stabilitydetermination flag FSMCSTAB is “1”. If the stability determination flagFSMCSTAB is “0”, indicating that the adaptive sliding mode controller 21is stable, the control gain F is set to a normal gain XKRCH in stepS262, and the reaching law input Urch is calculated from the followingequation (48), which is the same as the equation (10a), in step S263.

Urch=−F×σpre/b 1  (48)

If the stability determination flag FSMCSTAB is “1”, indicating that theadaptive sliding mode controller 21 is unstable, the control gain F isset to a predetermined stabilizing gain XKRCHSTB in step S264, and thereaching law input Urch is calculated according to the followingequation (49), which does not include the model parameter b1, in stepS265.

Urch=−F×σpre  (49)

In steps S266 and S267, it is determined whether the calculated reachinglaw input Urch is in a range defined between a predetermined upper limitvalue XURCHH and a predetermined lower limit value XURCHL. If thereaching law input Urch is in the range between XURCHH and XURCHL, theprocess immediately ends. If the reaching law input Urch is less than orequal to the predetermined lower limit value XURCHL in step S266, thereaching law input Urch is set to the predetermined lower limit valueXURCHL in step S268. If the reaching law input Urch is greater than orequal to the predetermined upper limit value XURCHH in step S267, thereaching law input Urch is set to the predetermined upper limit valueXURCHH in step S269.

As described above, when the adaptive sliding mode controller 21 becomesunstable, the control gain F is set to the predetermined stabilizinggain XKRCHSTB, and the reaching law input Urch is calculated withoutusing the model parameter b1, which brings the adaptive sliding modecontroller 21 back to its stable state. When the identifying processcarried out by the model parameter identifier 22 becomes unstable, theadaptive sliding mode controller 21 becomes unstable. Therefore, byusing the equation (49) that does not include the model parameter b1which has become unstable, the adaptive sliding mode controller 21 canbe stabilized.

FIG. 28 is a flowchart showing a process of calculating the adaptive lawinput Uadp, which is carried out in step S205 shown in FIG. 22.

In step S271, it is determined whether or not the stabilitydetermination flag FSMCSTAB is “1”. If the stability determination flagFSMCSTAB is “0”, indicating that the adaptive sliding mode controller 21is stable, the control gain G is set to a normal gain XKADP in stepS272, and the adaptive law input Uadp is calculated from the followingequation (50), which corresponds to the equation (11a), in step S273.

Uadp=−G×SUMSIGMA/b 1  (50)

If the stability determination flag FSMCSTAB is “1”, indicating that theadaptive sliding mode controller 21 is unstable, the control gain G isset to a predetermined stabilizing gain XKADPSTB in step S274, and theadaptive law input Uadp is calculated according to the followingequation (51), which does not include the model parameter b1, in stepS275.

Uadp=−G×SUMSIGMA  (51)

As described above, when the adaptive sliding mode controller 21 becomesunstable, the control gain G is set to the predetermined stabilizinggain XKADPSTB, and the adaptive law input Uadp is calculated withoutusing the model parameter b1, which brings the adaptive sliding modecontroller 21 back to its stable state.

FIG. 29 is a flowchart showing a process of determining the stability ofthe sliding mode controller, which is carried out in step S16 shown inFIG. 9. In this process, the stability is determined based on adifferential value of the Lyapunov function, and the stabilitydetermination flag FSMCSTAB is set according to the result of thestability determination.

In step S281, a switching function change amount Dσpre is calculatedfrom the following equation (52). Then, a stability determiningparameter SGMSTAB is calculated from the following equation (53) in stepS282.

Dσpre=σpre(k)−σpre(k−1)  (52)

SGMSTAB=Dσpre×σpre(k)  (53)

In step S283, it is determined whether or not the stabilitydetermination parameter SGMSTAB is less than or equal to a stabilitydetermining threshold XSGMSTAB. If SGMSTAB is greater than XSGMSTAB, itis determined that the adaptive sliding mode controller 21 may possiblybe unstable, and an unstability detecting counter CNTSMCST isincremented by “1” in step S285. If SGMSTAB is less than or equal toXSGMSTAB, the adaptive sliding mode controller 21 is determined to bestable, and the count of the unstability detecting counter CNTSMCST isnot incremented but maintained in step S284.

In step S286, it is determined whether or not the value of theunstability detecting counter CNTSMCST is less than or equal to apredetermined count XSSTAB. If CNTSMCST is less than or equal to XSSTAB,the adaptive sliding mode controller 21 is determined to be stable, anda first determination flag FSMCSTAB1 is set to “0” in step S287. IfCNTSMCST is greater than XSSTAB, the adaptive sliding mode controller 21is determined to be unstable, and the first determination flag FSMCSTAB1is set to “1” in step S288. The value of the unstability detectingcounter CNTSMCST is initialized to “0”, when the ignition switch isturned on.

In step S289, a stability determining period counter CNTJUDST isdecremented by “1”. It is determined whether or not the value of thestability determining period counter CNTJUDST is “0” in step S290. Thevalue of the stability determining period counter CNTJUDST isinitialized to a predetermined determining count XCJUDST, when theignition switch is turned on. Initially, therefore, the answer to stepS290 is negative (NO), and the process immediately goes to step S295.

If the count of the stability determining period counter CNTJUDSTsubsequently becomes “0”, the process goes from step S290 to step S291,in which it is determined whether or not the first determination flagFSMCSTAB1 is “1”. If the first determination flag FSMCSTAB1 is “0”, asecond determination flag FSMCSTAB2 is set to “0” in step S293. If thefirst determination flag FSMCSTAB1 is “1”, the second determination flagFSMCSTAB2 is set to “1” in step S292.

In step S294, the value of the stability determining period counterCNTJUDST is set to the predetermined determining count XCJUDST, and theunstability detecting counter CNTSMCST is set to “0”. Thereafter, theprocess goes to step S295.

In step S295, the stability determination flag FSMCSTAB is set to thelogical sum of the first determination flag FSMCSTAB1 and the seconddetermination flag FSMCSTAB2. The second determination flag FSMCSTAB2 ismaintained at “1” until the value of the stability determining periodcounter CNTJUDST becomes “0”, even if the answer to step S286 becomesaffirmative (YES) and the first determination flag FSMCSTAB1 is set to“0”. Therefore, the stability determination flag FSMCSTAB is alsomaintained at “1” until the value of the stability determining periodcounter CNTJUDST becomes “0”.

FIG. 30 is a flowchart showing a process of calculating the defaultopening deviation thdefadp, which is carried out in step S17 shown inFIG. 9.

In step S251 shown FIG. 30, a gain coefficient KPTH(k) is calculatedaccording to the following equation (54).

KPTH(k)=PTH(k−1)/(1+PTH(k−1))  (54)

where PTH(k−1) represents a gain parameter calculated in step S253 whenthe present process was carried out in the preceding cycle.

In step S252, the model parameter c1′ calculated in the process ofcalculations of the model parameter identifier as shown in FIG. 11 andthe gain coefficient KPTH(k) calculated in step S251 are applied to thefollowing equation (55) to calculate a default opening deviationthdefadp(k).

thdefadp(k)=thdefadp(k−1)+KPTH(k)×(c 1′−thdefadp(k−1))  (55)

In step S253, a gain parameter PTH(k) is calculated from the followingequation (56):

PTH(k)={1−PTH(k−1)}/(XDEFADPW+PTH(k−1))}×PTH(k−1)/XDEFADPW  (56)

The equation (56) is obtained by setting λ1′ and λ2′ in the equation(39) respectively to a predetermined value XDEFADP and “1”.

According to the process shown in FIG. 30, the model parameter c1′ isstatistically processed by the sequentialmethod-of-weighted-least-squares algorithm to calculate the defaultopening deviation thdefadp.

In the present embodiment, the model parameter identifier 22 shown inFIG. 3 corresponds to an identifying means, and the state predictor 23shown in FIG. 3 corresponds to a predicting means.

Although a certain preferred embodiment of the present invention hasbeen shown and described in detail, it should be understood that variouschanges and modifications may be made therein without departing from thescope of the appended claims.

What is claimed is:
 1. A control system for a throttle valve actuatingdevice including a throttle valve of an internal combustion engine andactuating means for actuating said throttle valve, said control systemincluding, predicting means for predicting a future throttle valveopening and controlling said throttle actuating device according to thethrottle valve opening predicted by said predicting means so that thethrottle valve opening coincides with a target opening, wherein saidthrottle valve actuating device is modeled to a controlled object modelwhich includes a dead time element, and said predicting means predicts athrottle valve opening after the elapse of a dead time due to said deadtime element, based on said controlled object model; and identifyingmeans for identifying at least one model parameter of said controlledobject model, wherein said predicting means predicts the throttle valveopening using the at least one model parameter identified by saididentifying means.
 2. A control system according to claim 1, furtherincluding a sliding mode controller for controlling said throttle valveactuating device with sliding mode control according to a throttle valveopening predicted by said predicting means, and identifying means foridentifying at least one model parameter of the controlled object model,wherein said sliding mode controller controls said throttle valveactuating device using the at least one model parameter identified bysaid identifying means.
 3. A control system according to claim 1,further including a sliding mode controller for controlling saidthrottle valve actuating device with a sliding mode control according toa throttle valve opening predicted by said predicting means.
 4. Acontrol system according to claim 3, wherein the control input from saidsliding mode controller to said throttle valve actuating device includesan adaptive law input.
 5. A control method for controlling a throttlevalve actuating device including a throttle valve of an internalcombustion engine and an actuator for actuating said throttle valve,said control method comprising the steps of: a) predicting a futurethrottle valve opening; and b) controlling said throttle actuatingdevice according to the predicted throttle valve opening so that thethrottle valve opening coincides with a target opening, wherein saidthrottle valve actuating device is modeled to a controlled object modelwhich includes a dead time element, and a throttle valve opening afterthe elapse of a dead time due to said dead time element, is predictedbased on said controlled object model; and c) identifying at least onemodel parameter of said controlled object model, wherein the throttlevalve opening is predicted using the identified at least one modelparameter.
 6. A control method according to claim 5, further comprisingthe step of identifying at least one model parameter of the controlledobject model, wherein said throttle valve actuating device is controlledwith a sliding mode control according to the predicted throttle valveopening, using the identified at least one model parameter.
 7. A controlmethod according to claim 5, wherein said throttle valve actuatingdevice is controlled with a sliding mode control according to thepredicted throttle valve opening.
 8. A control method according to claim7, wherein the control input to said throttle valve actuating deviceincludes an adaptive law input.
 9. A control system for a throttle valveactuating device including a throttle valve of an internal combustionengine and an actuator for actuating said throttle valve, said controlsystem including, a predictor for predicting a future throttle valveopening and controlling said throttle actuating device according to thethrottle valve opening predicted by said predictor so that the throttlevalve opening coincides with a target opening, wherein said throttlevalve actuating device is modeled to a controlled object model whichincludes a dead time element, and said predictor predicts a throttlevalve opening after the elapse of a dead time due to said dead timeelement, based on said controlled object model; and an identifier foridentifying at least one model parameter of said controlled objectmodel, wherein said predictor predicts the throttle valve opening usingthe at least one model parameter identified by said identifier.
 10. Acontrol system according to claim 9, further including a sliding modecontroller for controlling said throttle valve actuating device with asliding mode control according to a throttle valve opening predicted bysaid predictor, and an identifier for identifying at least one modelparameter of the controlled object model, wherein said sliding modecontroller controls said throttle valve actuating device using the atleast one model parameter identified by said identifier.
 11. A controlsystem according to claim 9, further including a sliding mode controllerfor controlling said throttle valve actuating device with a sliding modecontrol according to a throttle valve opening predicted by saidpredictor.
 12. A control system according to claim 11, wherein thecontrol input from said sliding mode controller to said throttle valveactuating device includes an adaptive law input.